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4:45 – 5:15 pm |
Session 18
– Preliminary Reports |
Marquis A |
The case of an undergraduate mathematics cohort of African
American males striving for mathematical excellence Christopher Jett Historically
Black Colleges and Universities (HBCUs) provide a different milieu as it
pertains to supporting students academically in all disciplines, and this
study champions an HBCU effort within the context of undergraduate
mathematics. Specifically, it highlights the case of a cohort of 16 African
American male mathematics majors at an all-male HBCU. The overarching
research question sought to delve deeper into these participantsÕ educational
experiences. Using qualitative research methods grounded in critical race
theory, preliminary data show that these African American male mathematics
majors were affirmed racially and mathematically in their undergraduate
mathematics space. 74 |
Marquis B |
Developing an open-ended linear algebra assessment: initial
findings from clinical interviews Muhammad Haider, Khalid
Bouhjar, Kelly Findley, Ruby Quea and Christine Andrews-Larson The
primary goal of this study was to design and validate a conceptual assessment
in undergraduate linear algebra course. We work toward this goal by
conducting semi-structured clinical interviews with 8 undergraduate students
who were currently enrolled or had previously taken linear algebra. We try to
identify the variety of ways students reasoned about the items with the
intent of identifying ways in which the assessment measured or failed to
measure studentsÕ understanding of the intended topics. Students were
interviewed while they completed the assessment and interview data was
analyzed by using an analytical tool of concept image and concept definition
of Tall and Vinner (1981). We identified two themes in studentsÕ reasoning:
the first theme involves students reasoning about span in terms of linear
combinations of vectors, and the second one involves students struggling to
resolve the number of vectors given with the number of entries in each
vector. 75 |
Marquis C |
Exploring tensions: LeanneÕs story of supporting
pre-service mathematics teachers with learning disabilities Robyn Ruttenberg-Rozen and
Ami Mamolo This
paper presents a case study of a mathematics teacher educator, Leanne, and
her story of trying to support the development of two pre-service elementary
school teachers with recognized learning disabilities. We analyze data
through a lens of mathematical knowledge for teaching, focusing in particular
on concerns and tensions about (i) maintaining academic rigor while meeting
the emotional, cognitive and pedagogical needs of her students, (ii)
seemingly opposing pedagogies between special education and mathematics
education practices, and (iii) equitable opportunities for teachers with
disabilities and the consequences for their potential pupils. We offer an
analysis of LeanneÕs personal struggle, highlighting implications for teacher
education and offering recommendations for future research. 83 |
Grand Ballroom 5 |
The Complement of RUME: What's Missing From Our Research? Natasha Speer and Dave
Kung The
Research in Undergraduate Mathematics Education (RUME) community has
generated a substantial literature base on student thinking about ideas in
the undergraduate curriculum. However, not all topics in the curriculum have
been the object of research. Reasons for this include the relatively young
age of RUME work and the fact that research topics are not necessarily driven
by the content of the undergraduate curriculum. What topics remain largely
untouched? We give a preliminary analysis, with a particular focus on
concepts in the standard calculus sequence. Uses for this kind of analysis of
the literature base in the education of novice researchers and potential
future directions for further analyses are discussed. 86 |
City Center A |
Exploring pre-service teachersÕ mental models of doing math Ben Wescoatt This
preliminary study explores the mental models pre-service teachers hold of
doing math. Mental models are cognitive structures people use while reasoning
about the world. The mental models related to mathematics would influence a
teacherÕs pedagogical decisions and thus influence the mental model of
mathematics that their students would construct. In this study, pre-service
elementary teachers drew images of mathematicians doing math and of
themselves doing math. Using comparative judgements, they selected an image
that best represented a mathematician doing math. Most images of
mathematicians doing math were of a man in front of a blackboard filled with
mathematical symbols. The mathematicians appeared happy. In contrast, many images
of participants showed them to be unhappy or in confused states. The
preliminary results suggest that their shared mental model of doing math is
na•ve and shaped by limited experiences with mathematics in the classroom. 90 |
City Center B |
ÔItÕs not an English classÕ: Is correct grammar an
important part of mathematical proof writing at the undergraduate level? Kristen Lew and Juan Pablo
Mejia-Ramos We
studied the genre of mathematical proof writing at the undergraduate level by
asking mathematicians and undergraduate students to read seven partial proofs
based on student-generated work and to identify and discuss uses of
mathematical language that were out of the ordinary with respect to what they
considered standard mathematical proof writing. Preliminary results indicate
the use of correct grammar is necessary in proof writing, but not always
addressed in transition-to-proof courses. 103 |